### Floored

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

### Getting an Angle

How can you make an angle of 60 degrees by folding a sheet of paper twice?

### Arclets Explained

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.

# Integral Polygons

##### Age 11 to 14 Short Challenge Level:
The greatest number of sides the polygon could have is $360$.

As each interior angle of the polygon is a whole number of degrees, the same must apply to each exterior angle. The sum of the exterior angles of a polygon is $360^{\circ}$ and so the greatest number of sides will be that of $360$-sided polygon in which each interior angle is $179^{\circ}$, thus making each exterior angle $1^{\circ}$.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.